complex number

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complex number:

see numbernumber,
entity describing the magnitude or position of a mathematical object or extensions of these concepts. The Natural Numbers

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their
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complex number

[′käm‚pleks ′nəm·bər]
Any number of the form a + bi, where a and b are real numbers, and i 2= -1.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

complex number

any number of the form a + ib, where a and b are real numbers and i = &#221A--1
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

complex number

A number of the form x+iy where i is the square root of -1, and x and y are real numbers, known as the "real" and "imaginary" part. Complex numbers can be plotted as points on a two-dimensional plane, known as an Argand diagram, where x and y are the Cartesian coordinates.

An alternative, polar notation, expresses a complex number as (r e^it) where e is the base of natural logarithms, and r and t are real numbers, known as the magnitude and phase. The two forms are related:

r e^it = r cos(t) + i r sin(t) = x + i y where x = r cos(t) y = r sin(t)

All solutions of any polynomial equation can be expressed as complex numbers. This is the so-called Fundamental Theorem of Algebra, first proved by Cauchy.

Complex numbers are useful in many fields of physics, such as electromagnetism because they are a useful way of representing a magnitude and phase as a single quantity.
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References in periodicals archive ?
The tasks that involved principles embodied the logic underlying the inversion, compensation, complex addition, and complex subtraction principles and principles pertaining to the properties of inequality relationships.
On the bottom line, unequal amounts are added to the equal amounts on the top line; the problem embodies the logic underlying the complex addition law.
In addition, significantly more fourth graders than second graders applied the complex addition principle ([chi square](1, N = 44) = 5.52, p = .019).
Since, a W-point FFT requires (W/2)log2(W) complex additions W[log.sub.2](W) complex multiplications [29], therefore the total number of operations for the FFT computation in the both the algorithms will be calculated as follows.
Complex Additions: [N/W][W/2][log.sub.2](W) [??] [N/2 [log.sub.2](W)]
While the number of complex additions and multiplications involved in the proposed methods are compared with that of SLM and PTS Schemes and tabulated in the Table 1.
The future holds even brighter and more complex additions to the automated information system.
The company continues to convince consumers they require ever-more bizarre and complex additions to the soles of their shoes, such as the Nike Shox.